We introduce a new simulation benchmark "HandoverSim" for human-to-robot object handovers. To simulate the giver's motion, we leverage a recent motion capture dataset of hand grasping of objects. We create training and evaluation environments for the receiver with standardized protocols and metrics. We analyze the performance of a set of baselines and show a correlation with a real-world evaluation. Code is open sourced at https://handover-sim.github.io.